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SUMMARY:Dispersive shock waves in coastal flows - Ted Johnson (University 
 College London)
DTSTART:20220712T130000Z
DTEND:20220712T133000Z
UID:TALK175853@talks.cam.ac.uk
DESCRIPTION:Coastal or boundary currents are an integral part of global oc
 ean circulation. For example\, currents may respond to external forcing or
  intrinsic instability by expelling vortex filaments or larger eddies into
  the ocean\, with implications for the mixing of coastal and ocean waters\
 ; and currents driven by outflows are important for the transport of fresh
 water\, pollutants and land-derived nutrients. There is also much interest
  in the behaviour of &lsquo\;free&rsquo\; fronts\, i.e. those that are far
  from the coast\, which can be used to model western boundary currents suc
 h as the Gulf Stream or the Kuroshio Extension. In the limit of rapid rota
 tion the governing equations reduce to the quasi-geostrophic equations - a
  modified form of the two-dimensional Euler equations. For the problems co
 nsidered here the vorticity of the flow is unity within the current and ze
 ro elsewhere. The unapproximated solution can thus be obtained numerically
  to high accuracy by applying the method of Contour Dynamics to the develo
 pment of the current-ocean interface. These solutions provide comparisons 
 for estimating the accuracy of asymptotic solutions.\nAlongshore variation
 s in the flows take place over scales large compared to offshore scales an
 d so analysis of the flows leads naturally to a long-wave equation for the
  current- ocean interface. Two examples will be discussed in depth. First\
 , the development of the flow when fluid is discharged from a source on th
 e coast to turn and form an alongshore current (Johnson et al. 2017) and\,
  second\, the Riemann problem for the subsequent development of a step cha
 nge in width of a coastal flow (Jamshidi & Johnson 2020).The flux function
  appearing in the long-wave equation is non-convex and this leads to a wid
 e variety of behaviours. Many of these are well-described following the me
 thod of El (2005) but some discrepancies remain. These and some other open
  questions will be noted.
LOCATION:Seminar Room 1\, Newton Institute
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